Why does <munderover> &#x2211;<!-- ∑ --> <mrow class="MJX-TeXAtom-ORD"> n

osmane5e

osmane5e

Answered question

2022-05-19

Why does n = 1 cos 1 n n diverge but n = 1 sin 1 n n converges?

Answer & Explanation

hoffwnbu

hoffwnbu

Beginner2022-05-20Added 13 answers

You have
sin ( 1 / n ) 1 / n
as n , so
sin ( 1 / n ) n 1 n 2
as n . This converges by the limit comparison test.
You have
cos ( 1 / n ) n 1 n
as n ; this series will diverge by the limit comparison test.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?